The purpose of this study is to see if intensive suppression of the immune system followed by replacement of the immune system with stem cells (the earliest, youngest cells in the bone marrow) stabilizes or improves the clinical condition of patients with systemic sclerosis (also known as scleroderma). Stem cell transplantation is a frequently used treatment for some types of cancer, such as leukemia and lymphoma. Stem cell transplantation has been performed in a small number of patients with both cancer and a co-existing autoimmune disease (rheumatoid arthritis, psoriasis, thyroid disease, systemic lupus erythematosus), but is an experimental therapy for patients with systemic sclerosis. In this study, we are using stem cells available in the blood stream. Compared to the use of actual bone marrow, the use of peripheral blood stem cells is associated with more rapid recovery of blood counts. An important initial goal of this study is to see how rapidly blood counts recover after intensive therapy and x-ray radiation and to establish the effects of such treatment in systemic sclerosis. Our initial experience with this treatment in 8 patients has provided two main findings. The first finding is that, at least with short term follow-up of less than 2 years, the disease activity can be suppressed and lead to less skin involvement with SSc. The second finding is that patients with serious lung disease from SSc are at risk of developing additional, serious lung damage after undergoing this experimental treatment. Two of the first eight patients died from lung damage. We believe this is related to underlying lung damage which cannot tolerate the high dose treatment. To reduce the risk of this complication we will substantially lower the dose of radiation administered to the lungs (to about one quarter of the previous dose), while keeping the remainder of the treatment the same.